This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Computer modeling of molecular signal cascades can provide useful insight into the underlying complexities of biological systems. We provide a refined approach of the discrete modeling of protein interactions within the environment of a single cell. The technique we offer utilizes the Membrane Systems paradigm which, due to its hierarchical structure, lends itself readily to mimic the behavior of cells. Since our approach is non-deterministic and discrete, it provides interesting contrast to the standard deterministic ordinary differential equations techniques. We argue that our approach may outperform ordinary differential equations when modeling systems with relatively low numbers of molecules - a frequent occurrence in cellular signal cascades. Refinements over our previous modeling efforts include the addition of nondeterminism for handling reaction competition over limited reactants, increased efficiency in the storing and sorting of reaction waiting times, and modifications of the model reactions. Results of our discrete simulation of the type I and type II Fas-mediated apoptotic signal cascade are illustrated and compared with two approaches: one based on ordinary differential equations and another based on the well-known Gillespie's algorithm.